The illustrations of steps shown in this proof will share the new key style:

black line = strong inference performed upon a set (strong link)

red line = weak inference performed upon a set (weak link)

black containers define a partioning of a strong set(s)

candidates crossed out in red = candidates proven false

Orange labels mark derived inferences

Blue circles indicate proven strong inference set result

Green circles indicate intermediate strong inference points

Other marks provided prn

Please be aware that, for me, strong and weak need not be mutually exclusive properties.

Step 3d prelude using Kraken cell transport.

Below, two of the three possible values of cell r9c7 are transported out to form a new
derived sis. This is very similar to the transportation of 3 of 4 values out of cell r7c9
that was performed as a prelude to step
2j. The entire deduction is
so symmetrical, in fact, that it becomes almost easy. Certainly, given step 2j, it
was easy to find.

Step 3d (2)r5c2=(6)r6c2

Not only is the Kraken transport symmetrical to that used in step 2j, but the conclusion
of that step and the conclusion of this step also have a very nice almost symmetrical aspect about
them. Furthermore, the entire argument is very similar, as demonstrated below.

2r5

c2

c8

2r7

c8

c6

2r3

c6

c4

6r5

c8

c4

1c4

r3

r5

r7

1c5

r8

r2

1B3

r2

r3c8

K3d

5*

3*

35*

3*

9r9c7

r6c7

2

9

3

r2c7

1

3

8

r2c3

8

3

3B4

r6

c3

r5c1

9c1

r9

r5

r6

6r6

c2

c6

c1

The conclusion of this step:

(2)r5c2=(6)r6c2 => r6c2≠2

All the 2's and all the 7's are then solved by hidden singles.

The puzzle is now solvable in myriad manners. To conserve space, I decided
to use a step that works quickly, but is more complex than the puzzle now warrants.

Step 4 prelude using guardian 5's and guardian sis transport.

Below, if candidate 5 is limited to the locations circled red, then a number of
impossible pentagons exist. Such overlap of impossible oddagons is usually the case if
one were to consider using guardians to derive sis. The possible locations for candidate 5
that are labelled with a green G form the guardian sis. However, since r8c7 is limited to
45, and since it sees four members of the guardian set, it is much more efficient to transport
the (4)r8c7 into the sis, and remove four of the 5's.

The guardian sis and transportation logic follows:

Guardian sis (5):[r1c4, r7c6, r8c13,r7c9,r9c7]

The AIC: (4=5)r8c7-(5):[r8c13,r7c9,r9c7]=(5)[r1c4, r7c6]

=> sis[(4)r8c7,(5)r1c4,(5)r7c6]

From this point, the deduction is fairly simple (for this puzzle!)

Step 4 chains transported guardian sis to derive (5)r1c4=(6)r5c4

Below, but for the trivalue transported sis and the double forbidding done by the potential
6 at r6c6, this would be nothing but a standard AIC. Finally, I am able, however, to transparently map all of
the weak inferences, and all but the transported guardian strong inference set.

Below find a short TM (triangular matrix) that performs precisely the same task.

6B5

r5c4

r6c6

6B4

r6

r4c1

4r4

c1

c3

4r1

c3

c7

1c6

r6

r7

TG

5r1c4

4r8c7

5r7c6

The conclusion: (5)r1c4=(6)r5c4 => r1c4≠6. This now solves many cells by naked
and hidden singles. All the sixes, all the ones, all the fours, and a few of the others.

Step 5 short skyscraper with candidate 9

Above, the standard run of the mill AIC:

(9): r5c3=r7c3-r7c9=r6c9 => r6c1≠9 & r5c7≠9

The puzzle now solves using only naked singles.

Easter Monster Solution

Parting Shots

This puzzle was more difficult than I care to tackle often. However, the ideas that it
forced upon me may prove to be useful in the future when faced with a puzzle devoid of
suitably bi-value, bi-location sis. The main ideas used herein, summarized:

Derived sis can be used again later. Even very complex ones help to focus searches.

Any tool in the toolbox is suitable for the creation of derived sis

Matrices are not only a useful tool for explaining a deduction, but
the concept of counting that they infer is useful in locating long, complex chain-like nets.

The matrix type, Mixed Block Matrix is an invention that can reduce matrix size. Although
Andrei and Bruno have proven that all sudoku eliminations can be justified using Block Triangular
Matrices, Mixed Block Matrices can significantly shorten the deductive path. Moreover, they
can more efficiently prove all of the derived sis available from one set of native sis. For this
reason, they show some promise towards a more efficient resolution of a puzzle such as the
Easter Monster. I am fairly certain that just such a more efficient and quicker solution
path exists for this puzzle. By quicker, I mean much quicker!

CONGRATULATION ! Thank you for your very very ... good work. But now very very... hard work for me and someone...

08/Dec/07 3:12 AM

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Hi ttt!

Thanks!

Not sure how good it is. It was difficult, though!

I am even more certain now of a better solution path, however - it adds a new wrinkle!

Hint: one more AUR not previously considered!

08/Dec/07 9:55 PM

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I would appreciate comments regarding www.stolaf.edu/people/hansonr/sudoku/easter_monster.htmwhich I believe to be a quite easy solution to the Easter Monster based on Medusa chains and a few new ideas.Bob Hansonhansonr@stolaf.edu